Daily Practice - Higher Plus

A histogram has two bars: one 20 units wide with frequency density 0.4, one 5 units wide with density 3.5. How many values in total?

A block has mass 470 g (to the nearest 10 g) and volume 5 cm³ (to the nearest cm³). Work out the upper bound of its density, to 2 decimal places.A block has mass 470 g (to the nearest 10 g) and volume 5 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.

Solve 5x² + 14x - 3 = 0.Solve 5x^2 + 14x - 3 = 0.

y is directly proportional to x². When x = 2, y = 20. Work out the positive value of x when y = 20.y is directly proportional to x^2. When x = 2, y = 20. Work out the positive value of x when y = 20.

The point (6, 8) lies on the circle x² + y² = 100. Work out the gradient of the tangent to the circle at that point.The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.